US8340294B2 - Secure modulation and demodulation - Google Patents
Secure modulation and demodulation Download PDFInfo
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- US8340294B2 US8340294B2 US12/008,709 US870908A US8340294B2 US 8340294 B2 US8340294 B2 US 8340294B2 US 870908 A US870908 A US 870908A US 8340294 B2 US8340294 B2 US 8340294B2
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
- H04L9/065—Encryption by serially and continuously modifying data stream elements, e.g. stream cipher systems, RC4, SEAL or A5/3
- H04L9/0656—Pseudorandom key sequence combined element-for-element with data sequence, e.g. one-time-pad [OTP] or Vernam's cipher
- H04L9/0662—Pseudorandom key sequence combined element-for-element with data sequence, e.g. one-time-pad [OTP] or Vernam's cipher with particular pseudorandom sequence generator
- H04L9/0668—Pseudorandom key sequence combined element-for-element with data sequence, e.g. one-time-pad [OTP] or Vernam's cipher with particular pseudorandom sequence generator producing a non-linear pseudorandom sequence
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04K—SECRET COMMUNICATION; JAMMING OF COMMUNICATION
- H04K1/00—Secret communication
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
Definitions
- the present invention relates generally to signal processing. More specifically, a technique for transmitting and receiving signals is disclosed.
- linear modulation techniques for encoding and decoding information. These techniques are typically amplitude and/or phase modulation techniques that map a symbol alphabet to a set of signals. For example, one of the simplest modulation techniques is pulse amplitude modulation (PAM), which maps a symbol alphabet ⁇ a 0 , a 1 , . . . , a N-1 ⁇ to N transmission levels.
- PAM pulse amplitude modulation
- Other examples of linear modulation techniques include phase shift keying (PSK) that maps the symbol alphabet to N phases, and quadrature amplitude modulation (QAM) that maps the symbol alphabet to both amplitude and phase shifted symbols.
- PSK phase shift keying
- QAM quadrature amplitude modulation
- FIG. 1 is a block diagram illustrating a transmitter embodiment.
- FIG. 2 is a block diagram illustrating a nonlinear keying modulator embodiment.
- FIG. 3 is a block diagram illustrating the details of a filter embodiment used by the nonlinear keying modulator shown in FIG. 2 .
- FIG. 4 is a block diagram illustrating a receiver embodiment.
- FIG. 5 is a block diagram illustrating a nonlinear keying demodulator embodiment.
- FIG. 6A is a block diagram illustrating a multi-stage transmitter embodiment.
- Linear modulator 600 modulates the input.
- FIG. 6B is a block diagram illustrating a receiver embodiment that corresponds to the transmitter shown in FIG. 6A .
- FIG. 7 is a flowchart illustrating the configuration process of a Slave device upon receiving the key, according to one embodiment.
- FIG. 8A is a plot illustrating the spectrum of an input sinusoid.
- FIG. 8B is a plot illustrating the spectrum of the output of a nonlinear keying demodulator embodiment, given the input shown in FIG. 8A
- FIG. 8C is a plot illustrating the spectrum of a nonlinear keying demodulator output with the input shown in FIG. 8B .
- FIG. 8D is a plot illustrating the time domain pulse amplitude modulated (PAM) signal input into a nonlinear keying modulator embodiment.
- PAM pulse amplitude modulated
- FIG. 8E is a plot illustrating the output of a nonlinear keying modulator embodiment, given the input shown in FIG. 8D .
- FIG. 8F is a plot illustrating the output of a nonlinear keying demodulator embodiment.
- the present invention can be implemented in numerous ways, including as a process, an apparatus, a system, or a computer readable medium such as a computer readable storage medium or a computer network wherein program instructions are sent over optical or electronic communication links. It should be noted that the order of the steps of disclosed processes may be altered within the scope of the invention.
- a technique for secure communication employs a nonlinear keying modulator in the transmitter to nonlinearly encrypt the signal, and a corresponding nonlinear keying demodulator in the receiver to decrypt the transmitted signal.
- a nonlinear keying modulator in the transmitter to nonlinearly encrypt the signal
- a corresponding nonlinear keying demodulator in the receiver to decrypt the transmitted signal.
- several cascaded nonlinear key modulators and demodulators are used in the transmitters and receivers, respectively.
- a key is exchanged between the transmitter and the receiver for the purpose of configuration.
- FIG. 1 is a block diagram illustrating a transmitter embodiment.
- Linear modulator 100 modulates the input linearly using amplitude and/or phase modulation, or any other appropriate techniques.
- the linearly modulated signal is sent to a nonlinear keying modulator (NKM) 102 , to be encrypted using a nonlinear keying modulation technique.
- the output of the NKM is then transmitted via channel 104 .
- the nonlinear keying modulation technique allows for many more permutations to be used for keying the amplitude and/or phase of the output signals, and also increases symbol dependency, making it difficult for eavesdroppers to decrypt the transmitted signal.
- the nonlinear modulation occurs after the linear modulation in the embodiment shown, the ordering of the modulators may be different in other embodiments. In some embodiments the nonlinear modulation occurs prior to the linear modulation.
- NKM nonlinear keying demodulator
- the receiver requires a corresponding nonlinear keying demodulator (NKD) to demodulate the received signal and undo the effects of the NKM.
- NTD nonlinear keying demodulator
- a technique for designing nonlinear filters and deriving their inverse is introduced by Batruni in U.S. patent application Ser. No. 10/418,944 entitled NONLINEAR INVERSION filed Apr. 18, 2003, which is incorporated herein by reference for all purposes.
- the NKM is designed as a nonlinear filter comprised of linear filters, nonlinear elements and a combination network connecting the linear filters and nonlinear elements.
- FIG. 2 is a block diagram illustrating a nonlinear keying modulator embodiment.
- the input is sent to a feedforward filter bank that includes feedforward filters 200 , 202 and 204 .
- the feedforward filters are combined with filters in a feedback filter bank, including feedback filters 206 , 208 and 210 , respectively, to form several pairs of linear filters.
- the outputs of the feedforward filters are summed with the outputs of the feedback filters to form the linear filters.
- a 1 ( z ), A 2 ( z ), A 3 ( z ) are used to denote Z-domain transfer functions for feedforward filters 200 , 202 and 204 , respectively, and B 1 ( z ), B 2 ( z ), B 3 ( z ) are used to denote transfer functions for feedback filters 206 , 208 and 210 .
- the corresponding linear filters formed by the pairs of feedforward and feedback filters are: A 1 ( z )/B 1 ( z ), A 2 ( z )/B 2 ( z ), A 3 ( z )/B 3 ( z ).
- the poles of the linear filters are determined by the transfer functions of the feedforward filters where as the zeros of the linear filters are determined by the transfer function of the feedback filters.
- Each of the linear filters is an infinite impulse response (IIR) filter.
- IIR infinite impulse response
- the feedback filters shown in FIG. 2 are absent, thus rendering the NKM a feedforward only system.
- the feedforward filters shown in FIG. 2 are absent, thus rendering the NKM a feedback only system.
- the summed outputs of the filter pairs are sent to a combination network 216 .
- the combination network connects the linear filters and the nonlinear elements such as the minimum-maximum processors.
- the combination network is a minimum-maximum switching matrix that connects a maximum processor 212 and a minimum processor 214 with the linear filters.
- a minimum or maximum processor also referred to as a minimum-maximum processor
- the processors are programmable to perform either the minimum function or the maximum function. It should be noted that the number of linear filters, minimum-maximum processors and their configurations are implementation dependent, and may vary in other embodiments.
- Each linear filter's poles and zeros govern the behavior of the system in an input signal subspace. Because the minimum-maximum processors effectively select one of the linear filters at a given point in the signal space, the set of poles and zeros of the selected linear filter govern the behavior of the system in the selected subspace where the linear filter is in effect. At a different point in the signal space, the selected linear filter and the corresponding set of poles and zeros may be different, resulting in different behavior of the system. The system behavior over the entire signal space is therefore nonlinear.
- the NKM can be made stable by keeping the poles of the linear filters to be inside the unit circle. Its bandwidth properties can be adjusted by adjusting the zeros of the linear filters. Thus, the NKM provides a nonlinear filter whose transfer characteristics, stability and bandwidth properties are controllable.
- FIG. 3 is a block diagram illustrating the details of a filter embodiment used by the nonlinear keying modulator shown in FIG. 2 .
- a filter may be used as the feedforward filter or the feedback filter.
- the input is scaled by a factor a 0 using a multiplier 300 .
- the input is also sent to a plurality of delay stages 302 , 304 , 306 and 308 .
- the delayed signals are scaled by coefficients of a 1 , a 2 , a 3 and a 4 .
- the scaled signals are combined by a combiner 314 .
- a constant value b 0 is added to the combined result via another combiner 310 to generate the output.
- a constant value is added to the scaled signals directly by combiner 304 , and thus combiner 310 is omitted.
- FIG. 3 illustrates a linear filter architecture that is commonly used, different types of linear filters may be employed in other embodiments.
- the number of coefficients and delay stages are chosen for the purpose of illustration, and may be different in some embodiments.
- FIG. 4 is a block diagram illustrating a receiver embodiment.
- the components in the receiver are arranged in reverse order of the transmitter components shown in FIG. 1 .
- An optional channel equalizer 400 is used to reverse the effects of the channel through which the signal is transmitted.
- a nonlinear keying demodulator (NKD) 402 performs the inverse function of the NKM in the transmitter.
- a linear demodulator 404 is used to perform phase or amplitude demodulation to recover the original input symbols.
- the ordering of the demodulators in the receiver may be different in other embodiments.
- FIG. 5 is a block diagram illustrating a nonlinear keying demodulator embodiment.
- the NKD circuitry is similar to the circuitry of the NKM; that is, the NKD is also comprised of linear filters and minimum-maximum processors combined by a combination network.
- the NKD is used to demodulate the signal modulated by the NKM shown in FIG. 2 , and has a transfer function that is the inverse of the nonlinear transfer function shown in Equation 3.
- X ( z ) [ B 3( z )/ A 3( z )] ⁇ [ B 2( z )/ A 2( z )]&[ B 1( z )/ A 1( z )] ⁇ Y ( z ) (Equation 4).
- the transfer functions of the linear filters formed by the feedforward and feedback filter pairs are inverses of the transfer functions of the linear filters in the NKM.
- the inverse transfer functions can be derived by replacing the poles in the original function with zeros, and zeros in the original function with poles.
- the coefficients of the feedforward filters and the coefficients of the feedback filters on the NKD are the reverse of the filter coefficients on the NKM.
- the coefficients of the feedforward filter correspond to the coefficients of the NKM's feedback filter
- the coefficients of the feedback filter correspond to the coefficients of the NKM's feedforward filter.
- a filter of the NKM includes a feedforward branch but not a feedback branch.
- the corresponding filter in the NKD has a feedback branch but not a feedforward branch, and the coefficients of the feedback branch correspond to the coefficients of the feedforward branches in the NKM.
- a filter of the NKM includes a feedback branch but not a feedforward branch.
- the corresponding filter of the NKD has a feedforward branch but not a feedback branch, and the coefficients of the feedforward branches correspond to the coefficients of the feedback branches in the NKD.
- the functions of the minimum-maximum processors are inverted in the inverse filter.
- the minimum processor in the NKM is replaced with a maximum processor in the NKD and the maximum processor in the NKM is replaced with a minimum processor in the NKD.
- switching filter coefficients and inverting the functions of the minimum-maximum processors provides an inverse filter that is used by the NKD to demodulate the transmitted signal.
- the poles of its linear filters are selected to be inside the unit circle. Since the zeros of the linear filters correspond to the poles of its inverse filter, the zeros of the linear filters of the NKM are also selected to be inside the unit circle so the inverse filters used in the NKD are stable.
- the filter configuration may be adjusted.
- the linear filter used in the NKM is a feedforward/feedback filter pair.
- the linear filter has a feedforward branch but no feedback branch; hence the corresponding inverse filter has a feedback branch but no feedforward branch.
- the filter is a filter with a feedback branch but no feedforward branch; hence the corresponding inverse filter has a feedforward branch but no feedback branch.
- the number of filter coefficients can be increased or decreased to change the complexity of the filters; the number of filters in the filter bank (i.e. the number of feedforward and feedback filter pairs) may be changed; the transmitter may include several NKM stages and thus the receiver includes several NKD stages that are the inverses of the NKM stages.
- FIG. 6A is a block diagram illustrating a multi-stage transmitter embodiment.
- Linear modulator 600 modulates the input.
- the linearly modulated signal goes through three cascaded stages of nonlinear keying modulation by NKM 602 , NKM 604 and NKM 606 .
- the multiple nonlinear keying modulation stages increase the depth of the nonlinear modulation and make the modulated signal more difficult to decode.
- FIG. 6B is a block diagram illustrating a receiver embodiment that corresponds to the transmitter shown in FIG. 6A .
- the received signal is demodulated by three NKD stages—NKD 650 , 652 and 654 , which correspond to the inverses of NKM 606 , NKM 604 and NKM 602 , respectively.
- the signal is sent to linear demodulator 656 and the symbols are recovered.
- the transmitter and/or the receiver may also include filters used to compensate the effects of the nonlinear channel through which the signal is transmitted.
- the transmitter and the receiver should be correctly configured in order for the receiver to successfully demodulate the transmitted signal and decode information.
- the demodulation performed by the receiver is the inverse operation of the modulation operation performed by the NKM.
- such a configuration is set up by exchanging a key between the transmitter and the receiver.
- the key includes parameters or any other appropriate information used to configure the receiver or the transmitter.
- a device referred to as the Master, initiates the exchange and sends the key to another device, referred to as the Slave.
- the slave receives the key and configures itself.
- the transmitter is the Master and the receiver is the Slave, thus the receiver configures itself according to the transmitter configuration.
- the transmitter is the Slave and the receiver is the Master, thus the transmitter configures itself according to the receiver configuration.
- the key includes topology information for deriving the topology of the nonlinear elements, the combination network, and the linear filters.
- the key also includes filter information for deriving the configurations of the linear filters, such as the pole-zero pairs of the filter banks.
- the key includes configuration information regarding the number of cascaded NKM or NKD blocks, and information regarding the following parameters for each block separately: the number of feedback filters and feedforward filters; the number of coefficients in each of the feedforward filters and feedback filters; the coefficients of the feedforward and feedback filters; and the topology of the minimum-maximum switching matrix connecting the feedforward and feedback filters.
- FIG. 7 is a flowchart illustrating the configuration process of a Slave device upon receiving the key, according to one embodiment.
- the coefficients of the feedback filters in the Slave are set to be the coefficients of the feedforward filters in the Master ( 700 ).
- the coefficients of the feedforward filters in the Slave are set to be the coefficients of the feedback filters in the Master ( 702 ).
- the minimum operations in the Master are configured as maximum operations in the Slave and vice versa ( 704 ). It should be noted that the ordering of the steps may be different in some embodiments. In certain embodiments, the steps take place in parallel. Unlike conventional security systems, the system does not require the receiver to be synchronized with symbols or code words sent by the transmitter. Once the key is exchanged between the transmitter and the receiver and the configurations are updated, the transmitter can commence transmission and the receiver is able to demodulate the raw channel output properly.
- FIG. 8A is a plot illustrating the spectrum of an input sinusoid.
- the signal is input into a nonlinear keying modulator embodiment.
- the sine wave input forms the peak at 800 .
- FIG. 8B is a plot illustrating the spectrum of the output of a nonlinear keying demodulator embodiment, given the input shown in FIG. 8A .
- the input signal is spread by the NKD in a nonlinear fashion and has a wider bandwidth.
- FIG. 8C is a plot illustrating the spectrum of a nonlinear keying demodulator output with the input shown in FIG. 8B .
- the NKD in this embodiment is the inverse of the NKM embodiment used for FIG. 8A , and thus the original signal is recovered by the demodulation process.
- FIG. 8D is a plot illustrating the time domain pulse amplitude modulated (PAM) signal input into a nonlinear keying modulator embodiment.
- FIG. 8E is a plot illustrating the output of a nonlinear keying modulator embodiment, given the input shown in FIG. 8D .
- the PAM symbols are scrambled in a nonlinear fashion by the NKD, and cannot be descrambled using conventional linear equalization, de-convolution or de-correlation techniques.
- FIG. 8F is a plot illustrating the output of a nonlinear keying demodulator embodiment.
- the NKD is the inverse of the NKM used to produce FIG. 8E . The plot shows that the NKD fully recovers the original symbols.
- a technique for secure communication employs a nonlinear key modulator in the transmitter to nonlinearly encrypt the signal, and a corresponding nonlinear key demodulator in the receiver to decrypt the transmitted signal.
- the resulting system provides good security, is stable, flexible and easy to implement.
Abstract
Description
Y=Min{X1,X2}=½[X1+X2−|X1−X2|] (Equation 1).
Y=Max{X1,X2}=½[X1+X2+|X1−X2|] (Equation 2).
Y(z)=[A3(z)/B3(z)]&{[A2(z)/B2(z)]^[A1(z)/B1(z)]}X(z) (Equation 3),
X(z)=[B3(z)/A3(z)]{[B2(z)/A2(z)]&[B1(z)/A1(z)]}Y(z) (Equation 4).
Claims (38)
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US13/555,783 US8829984B2 (en) | 2003-04-07 | 2012-07-23 | Secure modulation and demodulation |
US13/725,829 US9237007B2 (en) | 2003-04-07 | 2012-12-21 | Secure modulation and demodulation |
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US10/429,271 US7369658B2 (en) | 2003-04-07 | 2003-05-02 | Secure modulation and demodulation |
US12/008,709 US8340294B2 (en) | 2003-04-07 | 2008-01-10 | Secure modulation and demodulation |
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US13/725,829 Expired - Lifetime US9237007B2 (en) | 2003-04-07 | 2012-12-21 | Secure modulation and demodulation |
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US9237007B2 (en) | 2003-04-07 | 2016-01-12 | Broadcom Corporation | Secure modulation and demodulation |
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US7567631B2 (en) * | 2003-09-12 | 2009-07-28 | Neil Birkett | Method for amplitude insensitive packet detection |
US7532137B2 (en) * | 2007-05-29 | 2009-05-12 | Infineon Technologies Ag | Filter with capacitive forward coupling with a quantizer operating in scanning and conversion phases |
US8791792B2 (en) | 2010-01-15 | 2014-07-29 | Idex Asa | Electronic imager using an impedance sensor grid array mounted on or about a switch and method of making |
US8421890B2 (en) | 2010-01-15 | 2013-04-16 | Picofield Technologies, Inc. | Electronic imager using an impedance sensor grid array and method of making |
US8866347B2 (en) | 2010-01-15 | 2014-10-21 | Idex Asa | Biometric image sensing |
US20130279769A1 (en) | 2012-04-10 | 2013-10-24 | Picofield Technologies Inc. | Biometric Sensing |
US9455799B2 (en) | 2013-08-06 | 2016-09-27 | OptCTS, Inc. | Dynamic control of quality of service (QOS) using derived QOS measures |
US9444580B2 (en) | 2013-08-06 | 2016-09-13 | OptCTS, Inc. | Optimized data transfer utilizing optimized code table signaling |
US10523490B2 (en) | 2013-08-06 | 2019-12-31 | Agilepq, Inc. | Authentication of a subscribed code table user utilizing optimized code table signaling |
WO2016004185A1 (en) | 2014-07-02 | 2016-01-07 | OptCTS, Inc. | Data recovery utilizing optimized code table signaling |
CN107113163B (en) * | 2014-12-17 | 2021-01-22 | 瑞典爱立信有限公司 | Stream encryption technology |
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US9237007B2 (en) | 2003-04-07 | 2016-01-12 | Broadcom Corporation | Secure modulation and demodulation |
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US20140146967A1 (en) | 2014-05-29 |
US7369658B2 (en) | 2008-05-06 |
WO2004095723A3 (en) | 2005-10-20 |
WO2004095723A2 (en) | 2004-11-04 |
US8829984B2 (en) | 2014-09-09 |
US20040228488A1 (en) | 2004-11-18 |
US20080181402A1 (en) | 2008-07-31 |
US20120288094A1 (en) | 2012-11-15 |
US9237007B2 (en) | 2016-01-12 |
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